Question

The simple interest on a sum of money in 5 years at 12 % per annum is Rs. 400 less than the simple interest accrued on the same sum in 7 years at 10 % per annum. Find the sum.

Answer 1

Answer:

12x5=60%

7x10=70%

10%=400

100%=4000

Answer 2

The required  sum is  Rs. 4000.

Step-by-step explanation:

Given:

The simple interest accrued  on a sum of money in 5 years at 12 % per annum.

The simple interest accrued on the same sum in 7 years at 10 % per annum.

The simple interest in 5 years at 12 % per annum is Rs. 400 less than the simple interest in 7 years at 10 % per annum.

To Find :

The  required sum.

Formula Used:

$S=\frac{M\times p \times q}{100}$     ------------------ equation no.01.

S= simple interest

M= the original amount or  sum of money

p= the annual interest rate

q = the number of years

Solution:

As given- The simple interest accrued on a sum of money in 5 years at 12 % per annum.

                 p =12%      q= 5years

Putting the values of p and q in formula no. 01

Simple Interest    $S1=\frac{M\times 12 \times 5}{100}$  

                                 $=\frac{3M}{5}$    

  As given- The simple interest accrued on the same sum in 7 years at 10 % per annum.

                 p =10%      q= 7years

Putting the values of p and q in formula no. 01

Simple Interest   $S2=\frac{M\times 7 \times 10}{100}$

                                $=\frac{7M}{10}$

As given-   The simple interest in 5 years at 12 % per annum is Rs. 400 less than the simple interest in 7 years at 10 % per annum.

                           $S2-S1=400\\\frac{7M}{10} -\frac{3M}{5} =400\\\frac{7M- 6M}{10} =400\\7M-6M= 400 \times10\\M= Rs.\ 4000$

   Thus, the required sum is Rs. 4000.